Chapter 3.6, Problem 3P

Solve each compound inequality. Graph your solutions.

$5<k-2<11$

To determine

ToSolve:The compound inequality $5<k-2<11$ and graph the solution.

Answer to Problem 3P

The solutions of given inequality are all the real numbers in the interval $\left(7,13\right)$

The graph of the given inequality is

  

Explanation of Solution

Given:

Thecompound inequality $5<k-2<11$

Concept Used:

The solution of aninequality is the set of all the values which satisfies the inequality.

The graph of an inequality in one variable shows all the solutions of the inequality on a number line.

Calculation:

Given the compound inequality $5<k-2<11$

Solving it, we have

  $\begin{array}{c}5<k-2<11\text{ Add 2 into the inequality}\\ 5+2<k-2+2<11+2\\ 7<k<13\end{array}$

That is $k\in \left(7,13\right)$

Therefore, thesolution of given inequality are all the real numbers in the interval $\left(7,13\right)$

Graphing the solution of the given inequality.

Since, the solution of given inequality are all the real numbers $k$ , such that $k\in \left(7,13\right)$

Therefore, the graph of the given inequality is

  

Conclusion:

The solutions of given inequality are all the real numbers in the interval $\left(7,13\right)$

The graph of the given inequality is